# Stable Commutator Length

• Nicolaus Heuer (Oxford)
• Friday 16 November 2018, 15:00-16:00
• MR13.

Given a loop $\gamma$ in a topological space $X$. What is complexity of the surfaces needed to bound $\gamma$? This question may answered using the stable commutator length (scl) of $[\gamma] \in \pi_1(X)$. This invariant of group elements has many intriguing algebraic, geometric and analytic features.

I will introduce and motivate the theory of scl by giving highlight theorems and – most importantly – many open problems.

Finally, I will discuss a relation between scl in free groups and the l1-homology of one-relator groups. This is joint work with Clara Löh.

This talk is part of the Junior Geometry Seminar series.